Algebra and Applications Test 2

Consider the following statements:
1. ${\mathit{x}}^{\mathit{n}}+{\mathit{y}}^{\mathit{n}}$ is divisible by x + y if n = 2j + 1, where j is a positive integer.
2. ${\mathit{x}}^{\mathit{n}}-{\mathit{y}}^{\mathit{n}}$ is divisible by x - y if n = 2j, where j is a positive integer.
Which of the statements given above is/are correct?